Information Technology Reference
In-Depth Information
5.2 General Case
For each agent
a
, we have a subset of trust ratings, which we refer to as
T
P
OS
a
, such that:
1)
T
P
OS
a
T,
2)
If
Π
a
S
→a
(
τ
)
>
0
,
then
τ
⊂
T
P
O
a
,
∈
T
P
OS
a
3)
If
Π
a
S
→a
(
τ
)=0
,
then
τ
∈{
T
−
}
.
Each trust rating value in
T
P
OS
a
is possible. This means that the trust of agent
a
S
in
a
can possibly take any value in
T
P
OS
a
and consequently any trust rating
τ
∈
T
P
OS
a
can be
possibly associated with
τ
a
S
→a
. However, the higher the value of
Π
a
S
→a
(
τ
)
, the higher
T
P
OS
a
the likelihood of occurrence of trust rating
τ
∈
. We use the possibility distribution
of
Π
a
S
→a
(
τ
)
,
∀
τ
∈
T
to get the relative chance of happening of each trust rating in
T
P
OS
a
. In this approach, we give each trust rating
τ
, a Possibility Weight (PW) equal to:
PW
(
τ
)=
Π
a
S
→a
(
τ
)
/
τ
∈T
P
OS
a
Π
a
S
a
(
τ
)
.
(6)
→
Higher value of
PW
(
τ
)
implies more occurrences chance of the trust rating
τ
. Hence,
any trust rating
τ
T
P
OS
a
∈
is possible to be observed with a weight of
PW
(
τ
)
and
merged with
Π
a→a
D
(
τ
)
,
T
using one of the fusion rules.
Considering the General Case, there are a total of
∀
τ
∈
|
A
|
=
n
agents and each agent
a
T
P
OS
a
has a total of
|
|
possible trust values. For a possible estimation of
Π
a
S
a
D
(
τ
)
,
∀
τ
∈
→
T
P
OS
a
T
, we need to choose one trust rating of
τ
∈
for each agent
a
∈
A
.Having
T
P
OS
a
|
A
|
=
n
agents and a total of
|
|
possible trust ratings for each agent
a
∈
A
, we can
generate a total of
a∈A
|
T
P
OS
a
|
=
K
possible ways of getting the final possibility of
Π
a
S
→a
D
(
τ
)
,
T
. This means that any distribution out of
K
distributions is possible.
However, they are not equally likely to happen. If agent
a
S
∀
τ
∈
chooses trust rating
τ
1
∈
T
P
OS
a
1
T
P
OS
a
2
T
P
OS
a
n
for agent
a
1
,
τ
2
∈
for agent
a
2
, and finally
τ
n
for agent
a
n
∈
, then the
possibility distribution of
Π
a
S
→a
D
(
τ
)
,
∀
τ
∈
T
derived from these trust ratings has an
i
=1
n
Occurrence Probability(OP) of
PW
(
τ
i
)
.
For every agent
a
,wehave:
τ
PW
(
τ
)=1
, then considering all agents we have:
∈
T
P
OS
a
...
τ
n
∈T
P
OS
a
n
PW
(
τ
1
)
×
PW
(
τ
2
)
×
...
×
PW
(
τ
n
)=
.
(7)
τ
1
∈T
P
OS
a
τ
2
∈T
P
OS
a
2
1
As can be observed above, the
PW
is normalized in such a way that, for every set
of trust ratings
T
P
OS
a
i
), the corresponding OP of this set
can be measured through multiplication of
PW
of the trust ratings in the set, namely
PW
(
τ
1
)
{
τ
1
,τ
2
,...,τ
n
}
(where
τ
i
∈
×
PW
(
τ
2
)
×
...
×
PW
(
τ
n
)
.
5.3
Trust Event Coefficient
The
PW
(
τ
)
value shows the relative possibility of
τ
compared to other values in
T
of
an agent
a
. However, we still need to compare the possibility of a given trust rating
τ
,
